Problem: Fabio and Carlos play on a basketball team together. In the last game, Fabio had $7$ points less than $2$ times as many points as Carlos. Fabio scored $31$ points in the game. Write an equation to determine the number of points $(c)$ Carlos scored in the last game. Find the number of points Carlos scored in the last game.
Solution: Let $c$ be the number of points Carlos scored in the last game. $2$ times as many points as Carlos is equal to $2c$. Fabio had $7$ points fewer than $2c$. Fabio scored a total of $2c-7$ points. Since Fabio scored $31$ points, let's set this equal to $31$ : $ 2c-7=31$ Now, let's solve the equation to find the number of points $(c)$ Carlos scored in the last game. $\begin{aligned} 2c-7&=31\\ \\ 2c-7{+7}&=31{+7}&&{\text{add }7} \text{ to each side}\\ \\ 2c&=38\\ \\ \dfrac{2c}{{2}}&=\dfrac{38}{{2}}&&\text{divide each side by ${2}$}\\ \\ c&=19\end{aligned}$ The equation is $2c-7=31$. Carlos scored $19$ points in the last game.